Julius O. Smith
Scott A. Van Duyne
Ctr. for Comput. Res. in Music and Acoust. CCRMA), Dept of Music, Stanford Univ., Stanford, CA 94305
A new time-domain model for the piano is proposed which is extremely efficient for synthesizing piano sounds in hardware or software. The model includes multiple coupled strings, a nonlinear damped-spring hammer model, and a linear soundboard and enclosure component which can have arbitrarily large order at very low cost. Simplifications based on the commutativity of linear, time-invariant systems greatly reduce computational complexity [Comput. Music J. 74--91 (Winter 1992); Proc. International Computer Music Conference, Tokyo, pp. 56--71]. The hammer--string interaction is highly nonlinear and therefore does not commute with other components, in principle. However, by introducing a very mild approximation having little or no impact on the sound, commutativity can be achieved, leading to the enormous computational savings. This presentation will review the derivation of the piano synthesis model with special emphasis on the nonlinear hammer component. In its present form, a complete, two-key piano can be synthesized in real time on a single Motorola DSP56001 signal processing chip with 8K words of static RAM and a clock rate of 25 MHz.